Preheat the oven to 350 F. Line a couple of baking sheets with parchment paper and set aside.

In the bowl of a stand mixer fitted with the paddle attachment, combine the softened butter and sugar. Cream until smooth and combined.

Add the eggs and vanilla. Mix well, scraping down the sides of the bowl as needed.

Add the flour, cinnamon, and baking powder. Mix until a thick dough forms, scraping down the sides often.

In a small bowl, stir together the sugar and cinnamon for the coating. Reserve about 1 tablespoon of the mixture to sprinkle over the frosted cookies later.

Place the dough on the prepared baking sheets, leaving about 2 to 3 inches between each cookie. Use the bottom of a cup to flatten each cookie into a disk about 1/2 to 3/4 inch thick.

Bake for 10 to 12 minutes, or until the center is set and no longer looks wet. Let the cookies cool completely before decorating.

For the frosting, combine the softened butter, cinnamon, about half of the powdered sugar, and milk in the bowl of a stand mixer. Mix on low until combined.

Add the remaining powdered sugar and mix on low until combined. Increase the speed to medium and whip until smooth and fluffy. Add a small splash more milk only if needed to smooth it out.

Transfer the frosting to a piping bag.

Once the cookies are cool, pipe a spiral of frosting over the top of each cookie.

Sprinkle with a little of the reserved cinnamon sugar mixture before serving.